Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x+4y &= -4 \\ 5x+4y &= -8\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -5x-8$ Divide both sides by $4$ to isolate $y$ $y = {-\dfrac{5}{4}x - 2}$ Substitute this expression for $y$ in the first equation. $-4x+4({-\dfrac{5}{4}x - 2}) = -4$ $-4x - 5x - 8 = -4$ Simplify by combining terms, then solve for $x$ $-9x - 8 = -4$ $-9x = 4$ $x = -\dfrac{4}{9}$ Substitute $-\dfrac{4}{9}$ for $x$ back into the top equation. $-4( -\dfrac{4}{9})+4y = -4$ $\dfrac{16}{9}+4y = -4$ $4y = -\dfrac{52}{9}$ $y = -\dfrac{13}{9}$ The solution is $\enspace x = -\dfrac{4}{9}, \enspace y = -\dfrac{13}{9}$.